Abstract: The Levi operators are operator abstractions of the Levy property of Banach lattices. Such operators have been studied recently by several authors. The present paper deals with the collective properties of the Levi operators of several kinds: σ-Levi operators; quasi c-σ-Levi operators; and quasi σ-Levi operators. A notion of collectively σ-Levi set generalizes the notion of a single σ-Levi operator to the families of operators. Working with families of sequences of elements of a vector lattice requires the notion of the collective order convergence. This notion that is introduced and studied in the present paper may have its own interest and further possible applications. Various relations of the collectively quasi σ-Levi sets to the collectively compact sets are investigated. The domination problem for the collectively quasi σ-Levi sets is studied. In this study a special notion of a set of operators dominated by another set of operators is used.

Cite: Emelyanov E.Y.
On Collectively σ-Levi Sets of Operators
Владикавказский математический журнал (Vladikavkaz Mathematical Journal). 2025. V.27. N1. P.36-43. DOI: 10.46698/y6929-3405-2251-o OpenAlex

Dates:

Submitted:	May 22, 2024
Published print:	Mar 24, 2025
Published online:	Mar 24, 2025

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OpenAlex:

W4408620858

Citing: Пока нет цитирований

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